A parallel-plate capacitor with plate area \( A \) and separation distance \( d \) is connected in a circuit to a battery that maintains a constant potential difference \( V_0 \). Initially, there is a vacuum between the plates, and the capacitor is fully charged. A solid dielectric slab with dielectric constant \( \kappa \) (where \( \kappa > 1 \)) is placed just outside the plates. An external agent slowly pushes the slab into the capacitor until it completely fills the space between the plates. The capacitor remains connected to the battery during this entire process.